# math

Joe has a collection of nickels and dimes that is worth \$6.20. If the number of dimes was doubled and the number of nickels was decreased by 37, the value of the coins would be \$8.85. How many nickels and dimes does he have?

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1. original number of nickels : x
original number of dimes : y
5x + 10y = 620 or
x + 2y = 124 (#1)

new case:
number of nickels : 2y
number of dimes : x-37
5(x-37) + 10(2y) = 885
5x + 20y = 1070
x + 4y = 214 (#2)
subtract: #2 - #1
2y = 90
y = 45
sub into #1
x + 2(45) = 124
x = 34

He had 34 nickels and 45 dimes

check: 34nickels + 45 dimes = 170+450 = 620
case 2:
90 dimes + (-3nickels) = 900 - 15 = 885

Even though there is a mathematical solution , and the answer can be verified arithmetically, the answer
makes no real sense
So I would say there is no solution, and the problem as stated is flawed.

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